Question

Given (triangle) JKL, with side lengths JK=22 and KL=30, what are the possible lengths of JL?
Explain your reasoning

Answer 1

the location of all points of a third vertex would form a circle around a stick:

Answer 2

these are the 2 legs, one rotating about the connecting point

Answer 3

the shortest third leg possible is therefore the difference between the legs, and the longest possible is the sum of the legs. all other lengths range between these.

Answer 4

So?

Answer 5

its 13?

Answer 6

@amistre64

Answer 7

what is the difference in the legs? what is the sum of the legs?

Answer 8

30-22=?
30+22=?

Answer 9

13 and 52?

Answer 10

oh okay 52 - 13?

Answer 11

39

Answer 12

By the Triangle Inequality Theorem, one side of a triangle is less than the sum of the other two but greater than the positive difference.


So (30 - 22) < JL < (22 + 30)

Answer 13

What is 30 - 22 =

Answer 14

8

Answer 15

And, what is 22 + 30=

Answer 16

52

Answer 17

8 < JL < 52

Answer 18

JL could have lengths between but not including 8 and 52

Answer 19

Oh okay so lengths 9-51?

Answer 20

No

Answer 21

?

Answer 22

The lengths were not specified to be integers.
For all we know, JL could be 51.99

Answer 23

You are thinking in integers.

Answer 24

51 is not the greatest number less than 52. There is no such number.

Answer 25

JL could have lengths between but not including 8 and 52

which symbolically is this: 8 < JL < 52

Answer 26

Put this >>> okay so lengths 9-51? and you'll get it wrong.